Question

Quadrilateral ABCD has vertices A(-2,4), B(-3.-3), C(-5,-2), D(-5,2). Which of the following are the coordinates of A’ after a dilation centered at the origin with a scale factor of 2 1/2.

Answer 1

Answer:

$\boxed{A'(-5,10)}$

Step-by-step explanation:

Dilation is when you stretch something by the same amount in two perpendicular directions. In other words, dilation changes size, not overall shape. Dilation factors greater than one makes the shape greater while dilation factors less than one makes the shape smaller. The scale factor in this problem is:

$2\frac{1}{2}$

Which is a mixed fraction. This can be transformed into an improper fraction as follows:

$2\frac{1}{2}=2+\frac{1}{2}=\frac{4+1}{2}=\frac{5}{2}$

So the scale factor is $\frac{5}{2}$. Since the center of dilation is the origin, we just need to multiply each vertex of the quadrilateral by the scale factor. Thus, for A we have:

$A'(-2\times \frac{5}{2},4\times \frac{5}{2})=\boxed{A'(-5,10)}$